Foundations Of Transcomplex Numbers:

An extension of the complex number system to four dimensions

By E. Pérez

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Foundations of transcomplex numbers is a mathematics book about a novel way of extending the complex numbers system to four-coordinate variables, maintaining the usual operations attributed to the complex numbers.

The book is typeset in high quality Latex format for superb equations and text readability, formatted for 8½ x 11 letter size printing. With 194 pages, generously illustrated with 51 illustrations, and many cross-references like:

Table of Contents

Bibliography

Index

Index of Definitions

Index of Figures

Index of Nomenclature

Index of Theorems

Seven chapters divided as follows:

Ordered Pairs. The whole theory of transcomplex functions is based on the ordered pair concept: from the two-dimension plane up to the four-dimension space.

Complex Numbers. The complex numbers system is derived from the ordered pairs concept.

Transcomplex Numbers. Here starts the extension of the complex numbers into ordered pairs of complex numbers, arriving at the concept of transcomplexs.

The Coordinate System S4. This chapter is devoted to deriving a suitable coordinate system to plot transcomplex functions.

Transcomplex Functions. Functions of complex variables evolve to make space for functions of four-entries ordered pairs.

Transcomplex Surfaces. A radical and totally new perception of surfaces generated by complex variables.

Theorem Proofs. This chapter collects all the proofs of the theorems stated along the book.

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